Analytical formulation of the stability of finite-beta configurations

In a plasma column that is magnetically confined, the configuration of its isobaric surfaces changes as the ratio β = 8πp/B2 of its kinetic pressure to the magnetic pressure is increased toward finite values, as is the case, for instance, of a plasma column that is brought close to thermonuclear burn conditions. Then a major question is the stability of axisymmetric toroidal configurations against modes that can be driven unstable by the combined effects of the magnetic field curvature and the pressure gradient. Here attention is limited to the case where the plasma motion is tied to that of the magnetic field lines. Then it is argued that an increase of β will have a dual effect, because it not only increases the instability driving pressure gradient, but also enhances the stabilizing magnetic tension in that region of unfavorable curvature where the relevant modes develop